Analytical Study Guideline for Structural Health Monitoring of Steel Canister in Dry Cask Storage System by Using Multimodal Ultrasonic Lamb Waves

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1 Analytical Study Guideline for Structural Health Monitoring of Steel Canister in Dry Cask Storage System by Using Multimodal Ultrasonic Lamb Waves Ayman Kamal, Victor Giurgiutiu Department of Mechanical Engineering, University of South Carolina 3 Main St. Columbia, SC 2928 Tel:(83) , kamal@ .sc.edu,victorg@sc.edu Abstract Guided Lamb waves have been successfully used for some years as a monitoring technique for damage in plates and pipes. Multimodal Lamb waves are typically observed in thick structures, e.g. steel canisters in dry cask storage systems. Different modes have different sensitivity for certain types of cracks, and it is usually desired to excite specific symmetric or antisymmetric Lamb wave modes. To quantify the participation of different modes, it is important to know the power that each mode shares when exciting multiple modes. This study presents an analytical development and numerical simulations of wave power distribution between different ultrasonic Lamb wave modes using normal mode expansion (NME) technique. Piezoelectric wafer active sensor (PWAS) transducers were used to excite ultrasonic Lamb waves in the structure. The interaction between the PWAS and the structure was studied. Numerical simulations were performed for () thin aluminum plate (-mm) in which one symmetric and one antisymmetric modes exist, (2) thick steel plate (½") in which three symmetric and three antisymmetric modes exist. In the later case study, power partition between the 6 modes was presented, and a parametric study was performed for different transducer sizes and excitation frequencies. I. INTRODUCTION Nuclear power plants and radioactive waste systems are safety-critical facilities. These systems are in need of continuous scheduled inspection and preferably continuous structural health monitoring (SHM). It is crucial for monitoring structure performance and integrity, and detecting the initiation of flaws and damage in order to predict structural life and avoid catastrophic failures. There are many well-established techniques currently in operation in industrial facilities, for instance: ultrasonic testing/imaging and phased array technology, conventional and pulsed eddy current technique, vibration techniques, acoustic emission monitoring, and infrared thermography []. Ultrasonic testing/imaging is becoming one of the main practices for nondestructive evaluation (NDE) programs in aerospace, civil and nuclear industries [2]. Ultrasonic testing is used for inspecting weld flaws in solid structures [3], where imaging flaws using phased arrays and guided waves was presented. Comprehensive guidelines about ultrasonic guided waves for NDE and SHM for nuclear power plants can be found in [, 2, 4]. Developed inservice and preservice inspection programs are driven by requirements in the American Society of Mechanical Engineers Boiler and Pressure Vessel Code (ASME Code) and the requirements of the U.S. Nuclear Regulatory Commission (NRC) [4]. Many studies were performed for testing and monitoring pipeline in nuclear power plants. Ultrasonic wave propagation was used for detecting weld flaws, and wall thinning in stainless steel pipes and elbows [5]. Laser Doppler vibrometer was used for imaging wave propagation excited by lead zicronate titanate transducers. Another method for detecting wall thinning in stainless steel pipes is pulsed eddy current [6]. It was shown that pulsed eddy current testing is a promising technological approach to the NDE, and it has been principally developed for the measurement of surface flaws, subsurface flaws, and corrosion. Creep related damage in nuclear power plants were studied in [7]. Stress corrosion cracking (SCC) is another major flaw that initiates often in containers and piping systems with high corrosive materials or salt-water cooling systems. SCC mitigation and advanced detection methods were studied in one of the recent Los Alamos reports []. SCC is also a major concern for dry cask storage systems, and was observed in stainless steel canisters in dry cask storage systems with high levels of chlorine [8]. 224

2 (b) (a) (c) Figure. The various ways in which PWAS are used for structural sensing includes (a) propagating Lamb waves, (b) standing Lamb waves and (c) phased arrays. The propagating waves methods include: pitch-catch; pulse-echo; thickness mode; and passive detection of impacts and acoustic emission, [9]. PWAS: piezoelectric wafer active sensor. Dry cask storage systems are being used in the US and around the world for storing used nuclear fuel. It is essential to develop SHM systems that can assess the structure conditions in a timely manner without a human factor on site. The high levels of radiation occurred with Fukushima nuclear reactors, and the expected (4 years of clean up [2]), would require such systems for monitoring both nuclear facilities and high level waste storage systems. The Hanford site in Washington state has earlybuilt tanks made of carbon steel and not stainless steel; continuous monitoring of these tanks is very important. Although we stated earlier that ultrasonic guided waves is currently one of the lead techniques in NDE and SHM systems, there are many challenges using them, such as: () dispersion : every excited wave packet comprises waves with frequency spectrum and not a single frequency wave, these waves with different frequencies propagate at different speeds. Another challenge is (2) existence of multiple propagating modes at given exciting frequency from the source, e.g. function generator to generate ultrasonic Lamb waves into the structure. The objective of this study is to show the guidelines when multimodal Lamb waves exist in structure under test, which is typically the case for thick structures, e.g. steel canisters in dry cask storage systems. Piezoelectric wafer active sensor (PWAS) transducers have emerged as one of the major structural health monitoring (SHM) technologies because, with the same installation of PWAS transducers, one can apply a variety of damage detection methods (Figure ) (a) propagating ultrasonic guided waves, (b) standing waves (electromechanical E/M impedance ), as well as (c) phased arrays. PWAS is small, lightweight, unobtrusive, and inexpensive transducer. PWAS can act as a passive sensor, i.e. without interacting with the structure, and/or (3) an active sensor, where it interacts with the structure to detect the presence and intensity of damage. A characterization of PWAS transducers was studied in []. PWAS also helps achieving tuning of guided Lamb waves []. It was shown that energy loss of guided waves occur by existing flaws in the structure [2]. Impedance mismatch is considered an energy-stealing agent. Other studies [3, 4] gave more insights on how different defects interact with Lamb waves, and how the severity of impact damage can be predicted from the transmitted power. Generally, failure theories based on energy methods are more robust in predicting failure. In this study, we are analytically modeling Lamb wave modes power and presenting how modes share power. Then, we conclude by presenting parametric studies as optimization tools for power efficient SHM systems. 224

3 II. PWAS-STRUCTURE INTERACTION Normal mode expansion (NME) method is used to (a) find directly the amplitudes of given mode in terms of loading parameters, (b) evaluate the contribution factor of every mode to the total wave power and energy. Normal modes of the guided waves in the structure serve like the eigenfunctions [5]. Considering a PWAS of length 2a bonded to a structure of thickness 2d. Assuming pin-force model for PWAS-structure interaction, i.e. perfect bond (Figure 2), the developed shear stress by the PWAS is tx ()= x a [ ( xa) ( xa)] F ( )[ ( xa) ( xa)] where F ( ) is the force acting at the PWAS ends, and it is a function of excitation frequency applied to the PWAS. The model is a -D analytical model, and straight crested Lamb waves are assumed propagating in positive x- direction (forward waves) and negative x-direction (backward waves). Denoting structure particle motion by v, v for particle velocity in x and y directions, and T, T x y for axial and shear stresses respectively; power flow can be defined as [5, 6] d xx () Pmn yt y v yt y) 2 v n n n n x ( ) xx ( ) y ( ) xy( )dy (2) d where ( ) indicates the complex conjugate of the quantity, and m, n indicate Lamb wave mode number,2,3 xy Amplitudes of Lamb wave modes were normalized with respect to power flow and modal participation factor for the n th mode was defined as d PWAS v a ( x) F ( )[ e e ] e (3) n n x ina ina inx 4Pnn where a is half the PWAS length. is the propagating wave number, and it is the ratio between angular frequency and wave velocity ( c). Eq. (3) shows that the modal participation factor depends on characteristics of Lamb wave modes as well as transducer dimension. II. A. Electromechanical Admittance Impedance spectroscopy is commonly called for electromechanical (E/M) impedance of the transducer. However, the electrical admittance is commonly expressed to calculate the electrical power of the transmitter PWAS. The PWAS admittance when attached to the structure, i.e. the constrained PWAS admittance [9] is 2 YiC k3 r ( )cot ( ) where is the angular frequency, C is the capacitance, 2 2 E T k3 is the E/M coupling factor, a.k.a. k3 d3 / s 33 ; where d 3 is the piezoelectric coupling coefficient in 3 E T direction, s is the transducer compliance, 33 is the electrical permittivity of the transducer, ( ) ( )a ; where is the wave number, a is half the PWAS length, r is the dynamic stiffness ratio, r kstr / kpwas ; where k str was calculated by dividing the pin-force by the displacement field ux at the PWAS end. Displacement was determined from the NME solution with consideration of modal participation factor, Eq. (3). E PWAS stiffness is defined as kpwas tab/ sa; where t a is the PWAS thickness, b is the width. (4) II. B. Electrical Active power and Wave Power Figure 2. Pin force model for structurally-bonded PWAS, (a) PWAS pin forces at the ends on the upper surface, (b) developed shear stresses. Triggering the PWAS with electrical signal of voltage amplitude V ˆ ; and substituting the admittance from Eq. (4), the electrical power is evaluated as 2 2 P ˆ ˆ active YReV Preactive YImV (5)

4 The active power is the power that is converted to the mechanical power at the interface. The reactive power is the imaginary part of the complex power that is not consumed and is recirculated to the power supply. Mechanical power excites both forward and backward propagating waves initiating from the two end tips at x a and x a. Due to symmetry, we only need to consider the forward wave, which will contain only half of the mechanical power converted from the electrical active power. The time averaged wave power is p 2 T xx v x T xyv y da (6) A where A is the structure cross sectional area. Defining Sij as Lamb wave modes strain components, the timeaveraged kinetic and potential energies are ke. 4 vx v x v y. v y da A ve Txx 4 S xx T yys yy 2T xys xy da A It is worth mentioning that Equations (6) and (7) are defined for one single mode. Full length formula with modal participation factors of each mode and all involved parameters were reported in the Ref. [7]. In the next section we show numerical simulations for the developed wave power model. III. NUMERICAL SIMULATIONS We examplify power transaction between the PWAS and the structure with simulation of two plates, (a) -mm aluminum up to 2 khz, (b) 2.7-mm (½ in) steel up to 5 khz frequency of excitation. For both cases, harmonic excitation of volts was applied on a 7-mm PWAS. Complete listing of simulation parameters are in Table I, and Table II. For -mm aluminum case, impedance analyzer was used for measuring the transducer E/M impedance in complex form; then the admittance was calculated. The experiments were performed on multiple beams and plates to show the constrained PWAS resonances. Also the test was performed for constrained PWAS on the square aluminum plate of dimensions 24 mm x 24 mm x mm. The frequency sweep was up to 2 khz. As a validation for our developed analytical model, FEM simulations were performed using coupled field physics, where the PWAS was excited by voltage and the piezoelectric coupling introduces induced strains. Damping (7) was defined using complex compliance and complex electric permittivity with imaginary coefficients of.4. TABLE I Structure Simulations Parameters symbol 224 AL alloy steel-aisi-434 Length L thickness h mm 2.7 mm (½ in) Width b 7 mm 7mm Young s Modulus E 72.4 GPa 2 GPa Poisson ratio density Harmonic input voltage V ˆ V V amplitude Frequency sweep f -2 khz -5 khz TABLE II Transmitter PWAS (PZT85) properties (as from the company website symbol PZT85 Length l 5-25 mm thickness t a.2 mm Width b 7 mm Young s Modulus E 63 GPa Elastic compliance E s 5.8e-2 m 2 /N Relative dielectric T 33 / constant 75 Coupling coefficient k Piezoelectric coefficient d 3-75 nm/kv IV. RESULTS Comparison between analytical, experimental and FEM simulations are shown in Figure 3. The predicted first resonance was 34 khz by analytical model and FEM in which both do not account for the width dimension. The experimental result for the beam case was 25 khz, while it was 4 khz for the plate. The analytical model overestimated the admittance amplitude of the first resonance with respect to other resonances. Second resonance observed by FEM was 3 khz, (2 khz analytically and it was off experimentally - khz). Third resonance by FEM was 432 khz and it was missed by the analytical model; experimental results were khz. 2243

5 2 x -4 Admittance [/] (a) frequency [khz] (b) Figure 3. E/M admittance (a) analytical prediction, (b) experimental and FEM results [8] IV. A. Thin Structures (One Symmetric and One Antisymmetric Lamb wave modes) A parametric study was performed based on the analytical model of electrical active power for different PWAS sizes (5-25 mm) and frequencies (- khz). The results are presented as a 3D mesh plot (Figure 4). It indicated that active power generated from the PWAS to the structure contains the tuning effect of transmitter transducer size as well as the excitation frequency. The maximum active power in the simulation was 8.3 mw. This can be achieved by different combinations of PWAS and excitation frequencies, e.g. (5mm PWAS size and 6 khz, 9-mm PWAS and 89 khz). These combinations provide guidelines for the design of transmitter size and excitation frequency in order to obtain maximum wave power into the SHM structure. IV. B. Thick Structures (Multimodal Lamb waves) IV. B.. Power portioning between modes (7-mm PWAS size) Thick steel plate ½" thick and excited up to 5 khz was used as a case study in our predictive model, in which three symmetric and three antisymmetric modes exist. The structural particle velocities in x and y directions were reported in Ref. [7, 9] Power partitioning between the 6 modes is presented (Figure 5). Results show that: (a) S mode (the fundamental symmetric mode) has a rejection points 75 khz and 4 khz. (b) At 75 khz, A mode (the fundamental antisymmetric mode) absorbs all the energy leading to % for S mode. (c) The reported results represent the ratios of power between modes (Figure 5a). At 75 khz, S is rejected and A consumes all the power; however, at 2 khz, A actually consumes more power (than at 75 khz) (Figure 5b); this is due to the fact that our model is based on constant supplied electrical voltage. (d) A mode has a rejection point 4 khz. (e) At 4 khz, S power is dominant, i.e. it withdraws mostly all the energy, with a little share (less than %) by A mode, (f) At 28 khz, power is distributed almost equally between S, A, and A modes. IV. B. 2. Parametric study for multimodal Lamb waves (different PWAS sizes) Figure 4. Parametric study for electrical active power converted to wave power, for -mm aluminum simulation. A parametric study was performed on ½" thick steel plate. Different PWAS sizes (5-25 mm) were used, and excitation frequencies were (- khz). Figure 6 shows similar judicious combination of PWAS size and excitation frequency. A maximum value of electrical active power.6 mw could be obtained by 7-mm PWAS size and 576 khz excitation frequency, or 5-mm PWAS and 662 khz, or 24-mm PWAS size and 666 khz excitation. 2244

6 S A S A2 A2 A S S2 A S S S2 A (a) Figure 5. Power partitioning between modes for Lamb wave propagation in ½"- thick steel beam (a) normalized scale, (b) actual wave power in mwatt. (b) Figure 6. Parametric study for different PWAS transducer sizes and excitation frequencies for multimodal Lamb waves in thick steel structure. V. CONCLUSIONS Analytical investigation of power and energy transduction between PWAS and host structure was performed considering the exact Lamb waves. Predictive models were developed for Lamb wave power and energy using normal mode expansion technique. Input electrical active power is converted to mechanical power at PWAS interface; which in turn excites the guided waves. The PWAS power and energy study indicates that electrical active power, wave power and energies have the same tuning effect. Optimal energy coupling is a function of structure properties, geometry, PWAS size, and excitation frequency. The parametric studies give guidelines for maximum wave energy production for a given source of wave generation. ACKNOWLEDGMENTS This work is supported by Air Force Office of Scientific Research #FA , Program Manager, Dr. David Stargel; and the National Science Foundation under Grant # CMS

7 NOMENCLATURE a n (x) = modal-participation factor for n th mode d 3 = piezoelectric coupling coefficient in 3, m/v F (ω) = pin-force at PWAS ends k str = dynamic stiffness, N/m k 3 = electromechanical cross-coupling coefficient k e = time-averaged kinetic energy P mn = power factor. Measure of average power flow p = power, W p = time-averaged power r(ω) = dynamic stiffness ratio v e = time-averaged potential energy Y = admittance (simens) τ, τ a = shear stress at PWAS tip x = a REFERENCES [] J. A. TENCATE, T. J. ULRICH and N. R. BROWN, "Corrosion and Stress Corrosion Cracking: Recommendations for Mitigation and Advanced Detection," LA-UR Los Alamos National Laboratory, 22. [2] V. GIURGIUTIU and A. MENDEZ TORRES, "Opportunities and Challenges for Structural Health Monitoring of Radioactive Waste Systems and Structures," in 5th ASME Int. Conf. on Environmental Remediation and Radioactive Waste Management, Brussels, Belgium, Sep 8-2, 23. [3] T. STEPINSKI, "Ultrasonic nondestructive inspection of solid objects," in AIP Conf. Proc. 433,, 22. [4] S. R. Doctor, "Nuclear Power Plant NDE Challenges - Past, Present, and Future," in AIP Conf. Proc. 894, 7, 27. [5] J. R. LEE, H. JEONG, C. C. CIANG, D. J. YOON and S. S. LEE, "Application of ultrasonic wave propagation imaging method to automatic damage visualization of nuclear power plant pipeline," Nuclear Engineering and Design, vol. 24, no., pp , 2. [6] C. S. ANGANI, D. G. PARK, G. D. KIM, G. D. KIM and Y. M. CHEONG, "Differential pulsed eddy current sensor for the detection of wall thinning in an insulated stainless steel pipe," J. Applied Physics, vol. 7, pp. 9E72-4, 2. [7] G. SPOSITO, C. WARD, P. CAWLEY, P. B. NAGY and C. SCRUBY, "A review of non-destructive techniques for the detection of creep damage in power plant steels," NDT & E International, vol. 43, no. 7, pp , 2. [8] S. ETO, J. TANI, K. SHIRAI and T. FUJII, "Measurement of concentration of chlorine attached to a stainless-steel canister material using laser-induced breakdown spectroscopy," Spectrochimica Acta Part B: Atomic Spectroscopy, vol. 87, pp. 74-8, 23. [9] V. GIURGIUTIU, Structural Health Monitoring with Piezoelectric Wafer Active Sensors, Amsterdam: Elsevier Academic Press, 28. [] V. GIURGIUTIU and A. ZAGRAI, "Characterization of piezoelectric wafer active sensors," J.Intell. Mater. Sys. Struct., vol., pp , 2. [] V. GIURGIUTIU, "Tuned Lamb wave excitation and detection with piezoelectric wafer active sensors for structural health monitoring," J.Intell. Mat. Syst. Struct., vol. 6, pp , 25. [2] A. C. CHINTHALAPUDI and H. HASSAN, "Investigation of Methods to Detect Defects in Thin Layered Materials," Master's Degree Thesis, Blekinge Institute of Technology, Karlskrona, Sweden, 25. [3] D. N. ALLEYNE and P. CAWLEY, "The Interaction of Lamb Waves With Defects," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 39, no. 3, pp , 992. [4] Y. L. KOH, W. K. CHIU and N. RAJIC, "Effects of local stiffness changes and delamination on Lamb wave transmission using surface-mounted piezoelectric transducers," Composite Structures, vol. 57, pp , 22. [5] J. L. ROSE, Ultrasonic Waves in Solid Media, New York: Cambridge University Press, 999. [6] G. SANTONI, "Fundamental Studies in the Lamb- Wave Interaction Between Piezoelectric Wafer Active Sensor and Host Structure During Structural Health Monitoring," Dissertation, University of South Carolina, 2. [7] A. KAMAL, B. LIN and V. GIURGIUTIU, "Exact analytical modeling of power and energy for multimode Lamb waves excited by piezoelectric wafer active sensors," Journal of Int. Mat. Syst. Struct., vol. doi:.77/45389x34983, pp. - 2, 4 August 23. [8] A. KAMAL, B. LIN and V. GIURGIUTIU, "Optimizing Mode Tuning of Guided Waves and PWAS Electromechanical Impedance for Power Efficient SHM systems," in 9th International Workshop on Structural Health Monitoring, IWSHM, Stanford University, CA, Sep, -2, 23. [9] A. KAMAL, B. LIN and V. GIURGIUTIU, "Energy and power modeling of multi mode Lamb waves propagating in structure bonded with piezoelectric wafer active sensors," in AIP Conf. Proc. 5, 83,